Some Important Terms Used in Magnetism

Magnetic induction \[\vec B\] is the number of magnetic lines of induction crossing a unit area normally inside a magnetised substance.

Intensity of magnetisation is the magnetic moment per unit volume of a magnetised substance.

\[\vec H\] represents the magnetising influence of the applied external field. In practice, it can be controlled by changing the current in a coil or solenoid.

Magnetic permeability is the ratio of magnetic induction inside a substance to the magnetic intensity of the magnetising field.

Relative permeability is the ratio of the permeability of a substance to the permeability of free space.

Magnetic susceptibility measures how easily a substance becomes magnetised in an applied magnetic field.

\[\vec{M}=\frac{\vec{m}}{V}\]

where:

• \[\vec m\] = magnetic moment of the substance
• V = volume of the substance

SI Unit: A m⁻¹

\[{\vec{H}=\frac{\vec{B}}{\mu_0}-\vec{M}}\]

Equivalently, \[{\vec{B}=\mu_0(\vec{H}+\vec{M})}\]

μ = \[\frac {B}{H}\]

SI Units: T m A⁻¹ = N A⁻² = Wb A⁻¹m⁻¹

\[{\mu_r=\frac{\mu}{\mu_0}}\]

Alternatively, \[{\mu_r=\frac{B}{B_0}}\]

where B_0​ is the magnetic flux density in vacuum for the same magnetising field.

\[\vec M\] = χ_m​\[\vec H\]

\[\therefore\] χ_m = \[\frac {M}{H}\]

Meaning: When a substance is placed in an external magnetic field, it becomes magnetised. The actual magnetic field inside the substance is described by magnetic induction or magnetic flux density, \[\vec B\].

It is a vector. At a point, its direction is the direction of the magnetic field line there.

Key Ideas

• An iron bar placed parallel to a uniform external magnetic field becomes magnetised by magnetic induction.
• The induced field reinforces the external field inside the bar.
• Therefore, magnetic field lines become more concentrated inside a ferromagnetic bar.
• Outside the bar, the induced field opposes the applied field at some locations.

Units and Conversion

Permeability indicates how a material responds to a magnetic field and how much magnetic flux density is established in it for a given magnetic intensity.

Analogy: Think of permeability as a material’s magnetic response capacity. It is not literal “flow,” but it indicates how the material affects the magnetic field within it.

Derivation

• Start with: \[\vec{B}=\mu_0(\vec{H}+\vec{M})\]
• For a linear magnetic material: \[\vec{M}=\chi_m\vec{H}\]
• Substituting:
  \[\vec{B}=\mu_0(\vec{H}+\chi_m\vec{H})\]
  \[\vec{B}=\mu_0(1+\chi_m)\vec{H}\]
• But, \[\vec{B}=\mu\vec{H}\]
• Therefore, \[{\mu=\mu_0(1+\chi_m)}\]
• Dividing by μ₀​: \[{\mu_r=1+\chi_m}\]

Use this relation carefully: It is most useful for linear diamagnetic and paramagnetic materials. Ferromagnetic behaviour is generally non-linear.